A Well-Balanced and Positivity-Preserving Numerical Model for Shallow Water Flows in Channels with Wet–Dry Fronts

Abstract

In this paper, a novel well-balanced and positivity-preserving finite-volume method for the shallow water flows in open channels with non-uniform width and irregular bottom topography is developed. Special attentions are paid to guarantee the well-balanced property not only over the fully submerged domain, but also in those partially flooded and dry regions near the wet–dry interfaces. Such property is achieved via a new method involving local surface reconstruction and special discretization of the geometric source terms. The desired properties of the proposed numerical schemes are verified by a number of numerical experiments.